- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Quantifying quantum-amplified metrology via Fisher information

G. S. Agarwal1,2 and L. Davidovich1,3

  • 1Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
  • 2Departments of Biological and Agricultural Engineering and Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
  • 3Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-972, Brazil

PDF

Phys. Rev. Research 4, L012014 – Published 9 February, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012014

Abstract

We present a unified framework, based on quantum metrology concepts, for defining and quantifying deterministic noiseless quantum amplification of parameter-dependent processes, which plays an important role in increasing the precision of quantum sensing. Recent experiments [Burd et al., Science 364, 1163 (2019)] can be encompassed by this concept, which also leads to new suggestions of experimental work. The unified view presented here allows the identification of the basic steps for quantum amplification and of the measurements that lead to the best possible precision, beyond the quantum standard limit, in the estimation of parameters involved in the process. This is applied to the estimation of displacements of trapped ions and of the phase in SU(1,1) optical interferometers and atomic interferometry.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (42)

  1. H. A. Haus and J. A. Mullen, Quantum noise in linear amplifiers, Phys. Rev. 128, 2407 (1962).
  2. C. M. Caves, Quantum limits on noise in linear amplifiers, Phys. Rev. D 26, 1817 (1982).
  3. W. Wootters and W. Zurek, A single quantum cannot be cloned, Nature (London) 299, 802 (1982).
  4. D. Dieks, Communication by EPR devices, Phys. Lett. A 92, 271 (1982).
  5. V. Bužek and M. Hillery, Quantum copying: Beyond the no-cloning theorem, Phys. Rev. A 54, 1844 (1996).
  6. T. C. Ralph and A. P. Lund, Nondeterministic noiseless linear amplification of quantum systems, in Ninth International Conference on Quantum Communication, Measurement and Computing (QCMC), edited by A. Lvovsky, AIP Conf. Proc. NO. 1110 (AIP, New York, 2009), p. 155.
  7. G. Y. Xiang et al., Noiseless linear amplification and distillation of entanglement, Nat. Photon. 4, 316 (2010).
  8. H. A. Haus, Electromagnetic Noise in Quantum Optical Measurements (Springer, New York, 2000).
  9. R. Kakarla, J. Schröder, and P. A. Andrekson, One photon-per-bit receiver using near-noiseless phase-sensitive amplification, Light: Sci. Applic. 9, 153 (2020).
  10. S. C. Burd et al., Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019).
  11. D. Leibfried et al., Toward Heisenberg-limited spectroscopy with multiparticle entangled states, Science 304, 1476 (2004).
  12. M. Penasa, S. Gerlich, T. Rybarczyk, V. Metillon, M. Brune, J.M. Raimond, S. Haroche, L. Davidovich, and I. Dotsenko, Measurement of a microwave field amplitude beyond the standard quantum limit, Phys. Rev. A 94, 022313 (2016).
  13. R. Abbott et al., Observation of gravitational waves from two neutron star–black hole coalescences, ApJL 915, L5 (2021).
  14. V. Ménoret et al., Gravity measurements below 10−9g with a transportable absolute quantum gravimeter, Sci. Rep. 8, 12300 (2018).
  15. D. Kramer, DARPA looks beyond GPS for positioning, navigating, and timing, Phys. Today 67(10), 23 (2014); D. Feng, Review of quantum navigation, IOP Conf. Ser.: Earth Environ. Sci. 237, 032027 (2019).
  16. Boulder Atomic Clock Optical Network (BACON) Collaboration, Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature (London) 591, 564 (2021).
  17. K. A. Gilmore et al., Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science 373, 673 (2021).
  18. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976), Chap. VIII.4.
  19. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
  20. S. L. Braunstein and C. M. Caves, Statistical Distance and the Geometry of Quantum States, Phys. Rev. Lett. 72, 3439 (1994).
  21. B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nat. Phys. 7, 406 (2011).
  22. B. M. Escher, L. Davidovich, N. Zagury, and R. L. de Matos Filho, Quantum Metrological Limits via a Variational Approach, Phys. Rev. Lett. 109, 190404 (2012).
  23. M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, Quantum Speed Limit for Physical Processes, Phys. Rev. Lett. 110, 050402 (2013).
  24. C. L. Latune, B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Quantum limit for the measurement of a classical force coupled to a noisy quantum-mechanical oscillator, Phys. Rev. A 88, 042112 (2013).
  25. J. Wang, L. Davidovich, and G. S. Agarwal, Quantum sensing of open systems: Estimation of damping constants and temperature, Phys. Rev. Res. 2, 033389 (2020).
  26. M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. A. Walmsley, Experimental quantum-enhanced estimation of a lossy phase shift, Nat. Photon. 4, 357 (2010).
  27. R. A. Fisher, On the dominance ratio, Proc. R. Soc. Edinburgh 42, 321 (1922).
  28. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, NJ, 1946).
  29. C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, Bulletin Calcutta Math. Soc. 37, 81 (1945).
  30. K. C. MacCormick et al., Quantum-enhanced sensing of a single-ion mechanical oscillator, Nature (London) 572, 86 (2019).
  31. B. Yurke, S. L. McCall, and J. R. Klauder, SU(2) and SU(1, 1) interferometers, Phys. Rev. A 33, 4033 (1986).
  32. W. N. Plick, J. P. Dowling, and G. S. Agarwal, Coherent-light-boosted, sub-shot noise, quantum interferometry, New J. Phys. 12, 083014 (2010).
  33. J. Jing, C. Liu, Z. Zhou, Z. Y. Ou, and W. Zhang, Realization of a nonlinear interferometer with parametric amplifiers, Appl. Phys. Lett. 99, 011110 (2011).
  34. F Hudelist, J. Kong, C. Liu, J. Jing, Z. Y. Ou, and W. Zhang, Quantum metrology with parametric amplifier-based photon correlation interferometers, Nat. Commun. 5, 3049 (2014).
  35. B. E. Anderson, P. Gupta, B. L. Schmittberger, T. Horrom, C. Hermann-Avigliano, K. M. Jones, and P. D. Lett, Phase sensing beyond the standard quantum limit with a variation on the SU(1, 1) interferometer, Optica 4, 752 (2017).
  36. D. Leibfried et al., Creation of a six-atom “Schrödinger cat” state, Nature (London) 438, 639 (2005).
  37. P. Groszkowski, H.-K. Lau, C. Leroux, L. C. G. Govia, and A. A. Clerk, Heisenberg-Limited Spin Squeezing via Bosonic Parametric Driving, Phys. Rev. Lett. 125, 203601 (2020).
  38. L. Pezze, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
  39. G. S. Agarwal, Quantum Optics (Cambridge University Press, Cambridge, 2013), Sec. 5.22.
  40. M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
  41. G. S. Agarwal, R. R. Puri, and R. P. Singh, Atomic Schrödinger cat states, Phys. Rev. A 56, 2249 (1997).
  42. C. Song et al., Observation of multi-component atomic Schrödinger cat states of up to 20 qubits, Science 365, 574 (2019).

Outline

Information

Phys. Rev. Research 4, L012014– Published 9 February, 2022
  • Received 10 November 2021
  • Accepted 21 January 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation